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作者：Gravner, Janko; Lyu, Hanbaek; Sivakoff, David
作者单位：University of California System; University of California Davis; University System of Ohio; Ohio State University
摘要：Fix a simple graph G = (V, E) and choose a random initial 3-coloring of vertices drawn from a uniform product measure. The 3-color cycle cellular automaton is a process in which at each discrete time step in parallel, every vertex with color i advances to the successor color (i + 1) mod 3 if in contact with a neighbor with the successor color, and otherwise retains the same color. In the Greenberg-Hastings model, the same update rule applies only to color 0, while other two colors automaticall...
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作者：Pages, Gilles; Panloup, Fabien
作者单位：Sorbonne Universite; Universite d'Angers
摘要：We investigate a weighted multilevel Richardson-Romberg extrapolation for the ergodic approximation of invariant distributions of diffusions adapted from the one introduced in [Bernoulli 23 (2017) 2643-2692] for regular Monte Carlo simulation. In a first result, we prove under weak confluence assumptions on the diffusion, that for any integer R >= 2, the procedure allows us to attain a rate n(R/2R+1) whereas the original algorithm convergence is at a weak rate n(1/3). Furthermore, this is achi...
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作者：Ye, Heng-Qing; Yao, David D.
作者单位：Hong Kong Polytechnic University; Columbia University
摘要：Multiclass queueing networks (MQN) are, in general, difficult objects to study analytically. The diffusion approximation refers to using the stationary distribution of the diffusion limit as an approximation of the diffusion-scaled process (say, the workload) in the original MQN. To validate such an approximation amounts to justifying the interchange of two limits, t -> infinity and k -> infinity, with t being the time index and k, the scaling parameter. Here, we show this interchange of limit...
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作者：Chen, Yu-Ting
作者单位：University of Tennessee System; University of Tennessee Knoxville
摘要：We investigate stochastic spatial evolutionary games with death-birth updating in large finite populations. Within growing spatial structures subject to appropriate conditions, the density processes of a fixed type are proven to converge to the one-dimensional Wright-Fisher diffusions. Convergence in the Wasserstein distance of the laws of the occupation measures also holds. The proofs study the convergences under certain voter models by an equivalence between their laws and the laws of the ev...
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作者：Gnedin, Alexander; Iksanov, Alexander; Marynych, Alexander; Moehle, Martin
作者单位：University of London; Queen Mary University London; Ministry of Education & Science of Ukraine; Taras Shevchenko National University of Kyiv; Eberhard Karls University of Tubingen
摘要：Lambda-coalescents model the evolution of a coalescing system in which any number of blocks randomly sampled from the whole may merge into a larger block. For the coalescent restricted to initially n singletons, we study the collision spectrum (X-n,X- k : 2 <= k <= n), where X-n,X- k counts, throughout the history of the process, the number of collisions involving exactly k blocks. Our focus is on the large n asymptotics of the joint distribution of the X-n,X- k's, as well as on functional lim...
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作者：Frieze, Alan; Pegden, Wesley
作者单位：Carnegie Mellon University
摘要：In the Diffusion Limited Aggregation (DLA) process on Z(2), or more generally Z(d), particles aggregate to an initially occupied origin by arrivals on a random walk. The scaling limit of the result, empirically, is a fractal with dimension strictly less than d. Very little has been shown rigorously about the process, however. We study an analogous process on the Boolean lattice {0, 1}(n), in which particles take random decreasing walks from (1, ... , 1), and stick at the last vertex before the...
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作者：Krishnan, Arjun; Quastel, Jeremy
作者单位：University of Rochester; University of Toronto
摘要：The free-energy fluctuations of the discrete directed polymer in 1 + 1 dimensions is conjecturally in the Tracy-Widom universality class at all finite temperatures and in the intermediate disorder regime. Seppalainen's log-gamma polymer was proven to have GUE Tracy-Widom fluctuations in a restricted temperature range by Borodin, Corwin and Remenik [Comm. Math. Phys. 324 (2013) 215-232]. We remove this restriction, and extend this result into the intermediate disorder regime. This result also i...
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作者：Li, Yao
作者单位：University of Massachusetts System; University of Massachusetts Amherst
摘要：We consider a stochastic energy exchange model that models the 1-D microscopic heat conduction in the nonequilibrium setting. In this paper, we prove the existence and uniqueness of the nonequilibrium steady state (NESS) and, furthermore, the polynomial speed of convergence to the NESS. Our result shows that the asymptotic properties of this model and its deterministic dynamical system origin are consistent. The proof uses a new technique called the induced chain method. We partition the state...
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作者：Cheek, David; Antal, Tibor
作者单位：University of Edinburgh
摘要：First, we revisit the stochastic Luria-Delbruck model: a classic two-type branching process which describes cell proliferation and mutation. We prove limit theorems and exact results for the mutation times, clone sizes and number of mutants. Second, we extend the framework to consider mutations at multiple sites along the genome. The number of mutants in the two-type model characterises the mean site frequency spectrum in the multiple-site model. Our predictions are consistent with previously ...
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作者：Shneer, Seva; Stolyar, Alexander
作者单位：Heriot Watt University; University of Illinois System; University of Illinois Urbana-Champaign; University of Illinois System; University of Illinois Urbana-Champaign
摘要：We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated-ach node receives an exogenous flow of packets at the rate of. packets per time slot. Each packet takes one slot to transmit, but neighbouring nodes cannot transmit simultaneously. The algorithm we study is standard in the following sense: a node with an empty queue does not compete f...
